Help with XYZ math surface syntax
The problem was the abs function.

I opened up the script that creates the mesh ("..\Blender 2.82\2.82\scripts\addons\add_mesh_extra_objects\add_mesh_3d_function_surface.py"). It has a list of 'accepted' functions at the top and abs isn't included. However fabs is. When I changed the formula for X to fabs(cos(u))**0.8*a it worked as expected.